Survey of isospectral homogeneous Riemannian manifolds - Lauret, Emilio Agustin (2022)
We will review several results on inverse spectral geometry in the setting of homogeneous Riemannian manifolds.Somekey points will beSchueth’s examples ofcontinuous curves of isospectral left-invariant metrics on compact Lie groups, Sutton’s construction of isospectral compact homogeneous Riemannian manifolds(as a generalization of Sunada-Pesce’s method), and spectral isolation/uniqueness problems amongG−invariant metrics on a fixed homogeneous space G/K.